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Permanence for nonautonomous Lotka-Volterra cooperative systems with delays. (English) Zbl 1186.34119
Summary: We consider a class of nonautonomous two species Lotka-Volterra cooperative population systems with time delays, and establish sufficient conditions which ensure the system to be permanent.

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
Full Text: DOI
[1] Chen, L.; Lu, Z.; Wang, W., The effect of delays on the permanence for lotka – volterra systems, Appl. math. lett., 8, 71-73, (1995) · Zbl 0833.34071
[2] Lin, S.; Lu, Z., Permanence for two-species lotka – volterra systems with delays, Math. bio. eng., 3, 137-144, (2006), (electronic) · Zbl 1089.92059
[3] Lu, G.; Lu, Z., Global stability for \( n\) -species lotka – volterra systems with delay. II. reducible cases, sufficiency, Appl. anal., 74, 253-260, (2000) · Zbl 1016.92028
[4] Lu, G.; Lu, Z., Permanence for two species lotka – volterra cooperative systems with delays, Math. bio. eng., 5, 477-484, (2008) · Zbl 1158.92043
[5] Lu, Z.; Wang, W., Permanence and global attractivity for lotka – volterra difference systems, J. math. bio., 39, 269-282, (1999) · Zbl 0945.92022
[6] Muroya, Y., Uniform persistence for lotka – volterra-type delay differential systems, Nonlinear anal. RWA, 4, 689-710, (2003) · Zbl 1044.34035
[7] Saito, Y., The necessary and sufficient condition for global stability of a lotka – volterra cooperative or competition system with delays, J. math. anal. appl., 268, 109-124, (2002) · Zbl 1012.34072
[8] Xu, R.; Chen, L., Persistence and global stability for a delayed nonautonomous predator – prey system without dominating instantaneous negative feedback, J. math. anal. appl., 262, 50-61, (2001) · Zbl 0997.34070
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